To determine whether the sequence \( 5, 8, 12.8, 20.48 \) is arithmetic or geometric, we need to check for the respective properties of each type.
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Arithmetic Sequence: In an arithmetic sequence, the difference between consecutive terms is constant. We calculate the differences:
- \( 8 - 5 = 3 \)
- \( 12.8 - 8 = 4.8 \)
- \( 20.48 - 12.8 = 7.68 \)
The differences \( 3 \), \( 4.8 \), and \( 7.68 \) are not the same, so this is not an arithmetic sequence.
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Geometric Sequence: In a geometric sequence, the ratio between consecutive terms is constant. We calculate the ratios:
- \( \frac{8}{5} = 1.6 \)
- \( \frac{12.8}{8} = 1.6 \)
- \( \frac{20.48}{12.8} = 1.6 \)
Since the ratio is the same (1.6) for each pair of consecutive terms, this sequence is a geometric sequence.
In conclusion, the sequence \( 5, 8, 12.8, 20.48 \) is a geometric sequence with a common ratio of \( 1.6 \).
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